Finite volume solution of the unsteady free surface flow equations

[Abstract]: Water is a precious resource in much of Australia. Because of this, it is very important to be able to understand, control and manage this resource. One particular water intensive industry is the irrigation industry. Because of a very wide variety of irrigation methods it is hard to pick which is the most efficient or which can be developed into the most efficient. In aid to doing this, an unsteady free surface flow model is required. Many difficulties have been endured in developing a model that is accurate, versatile and robust enough to simulate many irrigation systems. Here the Finite Volume Method (FVM) gets investigated to find if it is a suitable method to be applied to these irrigation systems. The FVM is investigated by applying a pre-existing MatLab FVM model to a number of case studies. In doing this a series of adaptions need to take place to make the model more generalized so then it can be used to simulate a wider range of systems. The case studies look at the inclusion of differed boundary conditions, friction and bed slope, channel geometry, and dry channel bed conditions. It was found that the model was successful and proved versatile in modelling a very wide range of conditions throughout each case study. Comparing the valid steady state model outputs to results from the Mannings equation show the model has an average error of -0.019% for water flowing in downhill applications. To find the region where the model becomes inaccurate due to restrictions with the Mannings equation other situations were tested. It was found that for very low heights the comparison yielded very large errors. The threshold for model accuracy compared to the Mannings equation found inaccuracies at about 0.002m for a Mannings n value of 0.03, a bed slope of 2/1000, and a low flow rate. Other Mannings n values and bed slopes could be used to find other thresholds. This affects the size of the threshold that can be used and conflicts against the value recommended of 0.0001m in Bradford & Sanders (2002b). This model has been successful within the case studies although some limitations have been proven